Parton distribution functions and transverse momentum dependence of heavy mesons

Abstract

The leading Fock state light-front wave functions of heavy quarkonia and $D$ and $B$ mesons are obtained from the projections of their Bethe-Salpeter wave functions on the light front. We compute therefrom their leading-twist time-reversal even transverse momentum distributions and parton distribution functions. Mirroring the behavior of parton distribution amplitudes, the support of both distributions is increasingly narrower and shifted towards larger $x$ as a function of the meson mass. The dependence of $x$ and ${\text{k}}_{\perp }^2$ of the transverse distributions does not factorize into separate functions, and their fall-off with ${\text{k}}_{\perp }^2$ is much slower than that of light mesons.